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A metal sphere of radius 'R', density ' $\varrho_{1}$ ' moves with terminal velocity ' $\mathrm{v}_{1}$ ' through
a liquid of density ' $\sigma^{\prime}$. Another sphere of same radius but of density ' $\varrho_{2}$ ' moves
through same liquid. Its terminal velocity will be
Options:
a liquid of density ' $\sigma^{\prime}$. Another sphere of same radius but of density ' $\varrho_{2}$ ' moves
through same liquid. Its terminal velocity will be
Solution:
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Verified Answer
The correct answer is:
$\left[\frac{\mathrm{e}_{2}-\sigma}{\mathrm{e}_{1}-\sigma}\right] \mathrm{v}_{1}$
$6 \pi \eta R v_{1}=\frac{4}{3} \pi R^{3}(\rho_{1}-\sigma)$
$6 \pi \eta R v_{2}=\frac{4}{3} \pi R^{3}\left(\rho_{2}-\sigma\right)$
$\therefore \frac{v_{2}}{v_{1}}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma}$
$v_{2}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma} v_{1}$
$6 \pi \eta R v_{2}=\frac{4}{3} \pi R^{3}\left(\rho_{2}-\sigma\right)$
$\therefore \frac{v_{2}}{v_{1}}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma}$
$v_{2}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma} v_{1}$
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